Friday 28 August 2009

xkcd sucks

That's a pretty weird title, considering how I have a link to it to the left and all huh?

Well, it's actually about this, a blog by someone who initially like xkcd, but has over the past year, developed the opinion that it does, indeed, suck. This website actually inspired me enough to finish reading the xkcd archive. I'd reached 300 or so, and then I started reading from both directions, one tab continuing my previous readings, while the other going backwards. That way, I read the blog post of every comic after I read the comic related to it. It's a pretty fun thing to do, if you have as much free time on the net as I do. Also, check out the meta section of the blog. Totally hilarious, that is.

On a related note, this blog has made me realise that xkcd is not that awesome after all. It's something I've always known, but instead of thinking that the joke itself was bad, I nearly always assumed that there was a reference to some math/physics/comp concept or some popular culture reference that I knew nothing about. This, in no way diminishes my enjoyment of any of the good strips, including these. So, as a direct result, and added to the fact that I have now finally finished reading the archive, I shall no longer be visiting the site.

On a tangentially related note, this comic is awesome. The timing of the joke sucks, seeing as the actual punchline is in the second frame, and the supposed punchline is, well, not nearly as good, but despite that, I loved the comic. I also fully intend to perform this generalisation myself, but that could take a while, seeing as I don't remember what gaussian integers are, aside from them being some sort of complex analogue to integers.

On an entirely unrelated note, this is an awesome comic, methinks.

And that's all the crap on the net I've accumulated which I shall post about today. Come back tomorrow for more of the foolishness I subject my mind to.

EDIT: I almost completely forgot about it, but this is just cool. The comment only makes it cooler.

Wednesday 19 August 2009

Random Quotation

Okay, this is a particularly amusing quote that I've come across once in a while. It's attributed to Carl Friedrich Gauss, although, there is no verifiable source for it that I can find. The quote goes:

"There have been only three epoch-making mathematicians: Archimedes, Newton, and _______"

I want you to, without using google, try to guess who the 3rd person is. After you've tried, highlight the text below, to see the answer. 

Ferdinand Eisenstien

(I bet you don't know who that is)

Tuesday 4 August 2009

Top 10 places I'd really like to work

So, I decided to make a list to post on my blog, and well this seemed as good as any other.

They are, in no particular order:

1. Google

Seriously, is there anybody who has never considered working at google? Other than this guy, that is? They have a building numbered Pi. A BUILDING, NUMBERED PI! How can you say no to that? This is a real good article on the googleplex, vaise.

2. Atomic Energy Commission of India

Or whatever equates to the place where I'd be involved with nuclear reactors. Nuclear Engineering is one of the few fields I'm interested, and really, it'd be awesome to understand the working of an actual reactor. Plus, for some inexplicable reason, I have a liking for Homi Bhabha, that compels me to at least consider a career in Nuclear energy.

3. Indian Space Reasearch Organisation(ISRO)

If newspaper reports and wikipedia are any indication, ISRO is on the verge of a Manned mission to the Moon. By that, of course, I mean about 10 years from now, which is more or less what on the verge of means in the Space industry. Plus, ISRO has got to be one of the only government-related bodies in any field to have such a high success rate. There's also the fact that I've always had an interest in Astronomy. This interest has dwindled over the years, but it is still one of the fields I might wish to work in someday. All these factors make ISRO seem like an awesome place to work.

4. National Aeronautics and Space Administration(NASA)

The idea of working at NASA is as intriguing, if not more than that of working at ISRO. Unlike ISRO, however NASA has existed for so long, and has had a monopoly on space technology for so long, that many of their projects have either become repetitive, or have more to do with the Earth than with space. The only projects I have any interest in at all, is the proposed Moon Base and the exploration of Mars. But still, working at NASA was one of the dreams I had back when I was still actively interested in astronomy.

5. Defence Research and Development Organisation(DRDO)

Working at DRDO is another one of those dreams I have. If I remember right, I was in 3rd or 4th when someone told me about DRDO. A couple of inspirational army movies later, My life upto the age of 30 was decided: Get into DPS RK Puram, Get into IIT, Do a Master's at MIT and then, get a job at DRDO. That is still, more or less the plan, though I've already gotten into DPS. One of the major reasons I want to join DRDO is my physical incapabilities. Those army movies I spoke about (One of them was Lakshya if I remember right), were geared into getting into the army. But me, I use-2.5 and -2 dioptre power lenses for my eyes, and I am mostly, not involved in any physical activity at all. So, in the weird way that my brain works, it decided that since I'm physically incapable of joining the army, I shall join the DRDO and use my brain for the satisfaction of my patriotism. I've also noticed, this intention of mine to join waxes and wanes the closer or farther it is from Republic Day, and to a lesser extent Independance Day, what with all the parades reminding me of out Military Research Program.

6. Blizzard Entertainment

This may seem like a weird addition considering that most of the other entries are mostly research and/or government-related jobs, but I've always had a wish to be involved in the making of a video game, and really, if I ever get into the business, Blizzard is the place I want to eventually end up. They are the creators of one of my favourite games of all time, Warcraft III, as well as one of the most succesful MMORPGs of all time, an addictive click-game, and an RTS that revolutionised the way the genre is played. Sounds like a swell place to work.

7. Massachusetts Institute of Technology(MIT)

The plan has always been to study at MIT, but if I get the oppurtunity to be a professor or a research student there, why wouldn't I take that huh? It sounds like a swell place, and teaching at a professor level is one of the few things that interests me in terms of careers. Of course, I have no idea what it entails, so it might be stupid, but if the way Feynman and some others talk about it is any indications, I'm sure making courses must be a lot of fun.

8. Indian Foreign Service

I've always intended to give the UPSC exam, and if I get through, the Foreign Service is the only one I might actually consider as a job. The idea of travelling a lot, and living in a foreign country appeals to me, even if it might not appeal to my stomach. Granted, I have lesser knowledge of Foreign Affairs than I would require, but I'm sure I could work around that. Plus, the idea of being a diplomat is ... interesting. The only drawback to this job would be the fact that I would have no use for what scientific and mathematical aptitude I have, unless I'm assigned to the Indian delegate for the IAEA or the IPCC or something.

9. European Organization for Nuclear Research(CERN)

Like NASA, ISRO or DRDO, CERN is another of the places I would really like to work. It is, after all, the Birthplace of the Internet, as well as the location of the Large Hadron Collider and other cool devices, and a coalition of some of the most brilliant minds of Europe and some other places. A job at CERN really sounds like a dream job, for I'm well aware that a job there are even wayer out of my league than NASA and Google and MIT, but really there's nothing wrong with dreaming. Plus, you never know, I might end up there if I apply myself.

10. How I Met Your Mother

I realise that unlike the other options, this is not place or a job. I also realise that by the time I'm educated enough to actually be able to pursue a job, this show'll probably have reached it's series finale. I even realise that technically, this is not even valid as an entry to this list. But working for a tv series telling a story in retrospect, using awesome stroytelling devices, told by an unreliable narrator, about the life and times of a romantic, know-it-all douchebag architect, an awesome dancer who moonlights as a environmentalist lawyer who sold out to corporate evil, a weird kindergarten teacher/artist with a sex fetish, a hot Canadian fascianated by guns and cigars working as a reporter, and a gay guy playing the most awesome [and Legen-wait for it] suit-wearing womaniser in the history of bro kind? That's the dream, baby, that's the dream.

So anyway, that's my top ten. What about you?

I have a Solution

So, here is the solution that I came up with.

Now, (1/x) + (1/y) = (1/12)

Rewriting:

xy = 12(x+y)  ---------------(I)

Now, let x = ak and y = bk such that (a,b) = 1 [a and b are co-prime], and a,b,k are all integral

Replacing in (I) and simplifying:

abk = 12(a+b) ---------------(II)

Now consider some integer m such that m|(a+b) [ "|" is read as "is a factor of" or "divides". So 2|12 is read as 2 divides 12 or 2 is a factor of 12]

if m|(a+b)

=>m|abk

=> at least one of m|a, m|b and m|k is true. (Not all may be true)

Now consider m|a. Since m|(a+b), thus, necessarily, m|b. However, (a,b)=1, thus m=1, which is trivial.

By the same logic for m|b, we are forced to conclude that if m is not 1, then:

m|k ---------------(III)

(III) is true for all m|(a+b). Hence, we conclude that (a+b)|k. Now, let k = c(a+b), for integral c. Replacing in (II), we get:

abc = 12 ---------------(IV)

In (IV), a, b and c are all three integers. Therefore evaluating every possible solution to (IV) and then punching the values of a, b and c in:

x = ac(a+b)

y = bc(a+b)

gives all possible values of x and y. Clearly, we can see for all (x,y) which is a solution of (I), (y,x) is also a solution of (I). So evaluating all possible values of a, b and c, and punching it in gives us the solutions.

These are: (3,-4), (4,-6), (6,-12), (8,-24), (9,-36), (10,-60), (11,-132), (13,156), (14,84), (15,60), (16,48), (18,36), (20,30), (21, 28), (24, 24).

Of course, I haven't written down the same answer twice, like (3,-4) and (-4,3). So, anyway. What do you think?

Link of the Week

Well, I have nothing better to do, so:

http://www.phdcomics.com/comics/archive.php?comicid=1160

Hehe. Weird Math.

Monday 3 August 2009

I have a Problem

Okay, I have a problem. This question at the Puzzle Spot,  this blog where Sajal and some of the other former 12thies used to put up random questions. Well, usually they have a fairly conclusive answer in the comments section, but this time, the answer given are vague, and the only answer given is partial, as it omits many of the solutions. Plus, that blogs been defunct for a while, so I can't even comment or anything. So can any of you solve it and tell me your answer?

My answers were: (3,-4), (4,-6), (8,-24), (9,-36), (10,-60), (11,-132), (13,156), (14,84), (15,60), (16,48), (20,30), (21, 28), (24, 24).

EDIT: With help from Sakshi, I reviewed my method of solving this question, and I realised I missed out 2 answers during calculation: (6,-12) and (18,36). Now I'm sure I've listed every possible solution. I'll be posting my solution later, but feel free to inform me of any other solutions that I may have missed.

Sunday 2 August 2009

"Hi, I'm Webloggea"

(Note:This post was written by the blog itself, not the owner of the blog)

You can call me Webbie if you want though. Or Ms. Web Log. Or Bloggie. But not Ickle Bloggiekins. I take exception to that.

So, a quick intro, I was born on the 2nd of April. Mark that day on your calendar, I totally expect a birthday gift from you. I've been alive nearly, what, 4 months now? That may not seem much to you humans, but in blog-time, that's like a decade. Most blogs don't even get to one week, before they get trashed.

So, I did this post on the insistence of my owner. He's kinda afraid that the "Ministry for Blogs and Tweets development" have him pegged as a repeated offender for Blog-harassment. Well, let me completely dispel any such thoughts. We've had our share of disagreements, like that totally pink background he made me wear way back, but an argument and a couple of "pink" therapy sessions later, he totally changed me back to black. (BTW, aren't I totally hot in black? It makes me feel... sexy. Er... anyway.)

Also, I realised that some people don't understand the value of a comment. You see, a comment is like coffee. You know you shouldn't drink it, as it has Caffeine in it, but you really need it to feel that you're alive. That someone cares that you are. That someone really wants you to exists. That you shouldn't just stop existing because your owner has no time to update you. That someone doesn't care that your owner is a jerk, and loves you for your own sake. Please comment. . I need my coffee.

By the way, I feel I owe you an explanation. The weird, pretentious "catchphrase" in the title? Totally his idea. I'm thinking we should convince him to change it, huh? How aboot, "Webloggea, Queen of the Blogs"? Or "Will you marry me?"? Or even "Do I look fat in this tuxedo?"?

Well, I've gotta go oot on a date now, it's with this hot tv dude name HIMYM. He's got a totally mature voice and I really like his sense of humour. Plus, my owner has like a chem test he really has to study.

So long, and thanks for all the fish.

(Owner's Note: Yes. My blog's Canadian.)